This this is a previous animation I did a while ago. Since then, I have been able to fix the fluent movements within the animation. but when it comes down to it I'm still having trouble with the shading in the animation for the game.

The color looks good, but as you pointed out, the shading needs some attention. To start, it's not that bad so take heart. I'd darken the value or tonal aspect of the shadow slightly, and try and confine it to specific shapes. Shadows should read as shapes that help define the form of the subject that's affected by light. That's the biggest problem I see with your work, is that the shadows are not shapes as distinct as the forms themselves. Give it another try along those lines and see what kind of results you get.